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President Obama and Mitt Romney brought full quivers of statistics and factoids to the first battle of the general election, but both occasionally misfired — stretching the truth or omitting important context.

Romney made the case that his term as a Republican governor in Massachusetts would enable him to break the partisan gridlock in Washington.

“I had the great experience — it didn’t seem like it at the time — of being elected in a state where my Legislature was 87 percent Democrat,” Romney said during Wednesday’s debate in Denver. “And that meant I figured out from Day One I had to get along, and I had to work across the aisle to get anything done.”

Romney deserves credit for leading one of the most significant bipartisan initiatives in state history — the passage of a health care law in 2006 that has promoted near-universal insurance coverage. Romney’s plan, on which Obama modeled the Affordable Care Act of 2010, won the support of Democratic Senator Edward M. Kennedy
.

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But Romney’s work on health care was more an exception than the rule during his four years on Beacon Hill. Many Democrats who served in the Legislature during that time have described Romney as disengaged, treating lawmakers as if they worked for him and sometimes not bothering to learn their names.

The Obama campaign has used to its advantage the discontent of many Massachusetts Democrats. This week, 11 who overlapped with Romney have campaigned for Obama in nine swing states; since June, about two dozen current and former elected officials from Massachusetts have held more than 100 events in 11 states, where they have criticized Romney’s Bay State record.

During the debate, Obama attacked Romney for another health care plan — his proposed introduction of a Medicare voucher program in 2023.

“The problem is that because the voucher wouldn’t necessarily keep up with health care inflation, it was estimated that this would cost the average senior about $6,000 a year,” Obama said.

The additional cost estimate is an Obama campaign favorite, but it is outdated. It comes from a Congressional Budget Office report on the 2011 version of a Medicare plan by Romney’s running mate, Representative Paul Ryan of Wisconsin. That plan tied the value of the vouchers to inflation, which is expected to rise more slowly than health insurance costs, leaving future seniors to pay the difference out of pocket.

Romney’s plan, similar in ways, does not limit the vouchers’ value — though he has not ruled out a cap.

Romney hit back on health care, charging that “the CBO says up to 20 million people will lose their insurance as Obamacare goes into effect next year.” But that number represents the upper limit of the
office’s projection, and it is not an estimate for next year. The most likely scenario, according to the office, is that 3 to 5 million people will be moved off employer-sponsored insurance between 2019 and 2022.

While these people will “lose their insurance” in the sense that they will no longer have the same plans as they did before, many will qualify for Medicaid or government-subsidized private insurance.

Romney also did not mention that under the 20-million-person scenario, the
budget office estimated that the cost of the Affordable Care Act would go down “because the extra costs for Medicaid and exchange subsidies are more than offset by the increased revenues resulting from higher taxable compensation among workers who receive higher wages in lieu of health benefits.”

In another criticism of Obama’s health care law, Romney said no regulation was necessary for families to cover children as old as 26 on their insurance plans.

“That’s already offered in the private marketplace,” he said.

But a report issued in June by the Department of Health and Human Services showed that 3.1 million young adults had been able to join their parents’ plans because of the new law. The agency concluded that the proportion of insured adults ages 19 through 25 rose from 64 percent to about 75 percent as a result of the law.

Another survey, by the Commonwealth Fund, said as many as 6.6 million people in that age group had been provided access to insurance, though not all of those were uninsured before.

On deficit reduction, both made exaggerated claims. Obama said he has “put forward a specific $4 trillion deficit reduction plan.” But a quarter of the reduction is money saved by drawing down the military presence in Iraq and Afghanistan.

“There are a number of good policies in this budget, but the use of this war gimmick is quite troubling,” Maya MacGuineas, president of the bipartisan Committee for a Responsible Federal Budget, wrote in February. “Drawing down spending on wars that were already set to wind down and that were deficit-financed in the first place should not be considered savings.”

Romney asserted that “the president said he’d cut the deficit in half. Unfortunately, he doubled it. Trillion-dollar deficits for the last four years.”

Romney’s claim that Obama “doubled” the deficit is true — and actually understated — in a simple comparison between $459 billion in fiscal 2008 and $1.4 trillion in 2009. But the 2009 fiscal year began while George W. Bush was still president, and the budget for the year was largely set before Obama took office.

Two weeks before Obama’s inauguration, the Congressional Budget Office projected a $1.2 trillion deficit for fiscal 2009. Since the final deficit was $1.4 trillion, Obama might be blamed fairly for adding to — but not doubling — the deficit.

The deficit projection for the current fiscal year is $901 billion, about $500 billion less than the deficit during Obama’s first year in office but not the 50 percent reduction he promised.

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